1. Field of the Invention
The present invention relates to a command value decision unit for constructing and controlling a plant model so that the operation expense such as fuel cost of interlinked plants is made minimum under the constraint of keeping constant the total output of the plants.
2. Description of Related Art
FIG. 16 is a block diagram showing a conventional command value decision unit. In this figure, the reference numeral 1 designate a fuel consuming characteristic model generator which collects data about fuel consumption Q.sub.m for the output P.sub.m of each of interlinked plants G.sub.m, and which generates a fuel consuming characteristic model F.sub.m associated with each plant G.sub.m ; 2 designates a memory for storing the fuel consuming characteristic models F.sub.m generated by the fuel consuming characteristic model generator 1; 3 designates a differential calculator for differentiating the fuel consuming characteristic model F.sub.m associated with each plant G.sub.m by the output P.sub.m of that plant G.sub.m ; and 4 designates a command value calculator which calculates the output P.sub.m of each plant G.sub.m such that the respective derivatives dF.sub.m /dP.sub.m obtained by the differential calculator 3 coincide under the constraint that the sum total of the outputs P.sub.m of the plants G.sub.m agrees with an estimated load amount L, and makes the calculation results as the output command values P.sub.m * of the plants G.sub.m.
Next, the operation will be described.
First, the fuel consuming characteristic model generator 1 collects data about the fuel consumption Q.sub.m of the output P.sub.m of each of the interlinked plants G.sub.m. Thus, if m-plants are interlinked, the data are collected for each of them.
For example, as shown the diagram of FIG. 17, the data for one day from 12 o'clock at night to the next midnight are collected. The fuel consuming characteristic model generator 1, having collected the data, generates the fuel consuming characteristic model F.sub.m associated with each plant G.sub.m by modeling the fuel consumption Q.sub.m for the output P.sub.m of each plant G.sub.m using the following quadratic function. EQU F.sub.m =Q.sub.m =aP.sub.m.sup.2 +bP.sub.m +c (1)
where the values of the coefficients a, b and c are determined such that they best represent the actual characteristics using the least squares method or the like.
When the fuel consuming characteristic model generator 1 generates the fuel consuming characteristic model F.sub.m of each plant G.sub.m, the memory 2 stores them. In the following description, it is assumed for brevity and convenience that three plants G.sub.1, G.sub.2 and G.sub.3 are interlinked as shown in FIG. 18, and a method will be described for making decision of the output command values P.sub.1 *, P.sub.2 * and P.sub.3 * of the plant G.sub.1, G.sub.2 and G.sub.3 using a fixed-incremental fuel cost method which is disclosed, for example, in "Power System Engineering", pp. 262-273, published by Corona Publishing Co. Ltd, 1977.
The following equations are assumed as the fuel consuming characteristic models F.sub.1, F.sub.2 and F.sub.3 of the plants G.sub.1, G.sub.2 and G.sub.3 (see, FIGS. 19A-19C). EQU F.sub.1 =2P.sub.1.sup.2 +3P.sub.1 +1 (2) EQU F.sub.2 =P.sub.2.sup.2 +4P.sub.2 +2 (3) EQU F.sub.3 =P.sub.3.sup.2 +P.sub.3 +6 (4)
Once the fuel consuming characteristic models F.sub.1, F.sub.2 and F.sub.3 of the plants G.sub.1, G.sub.2 and G.sub.3 have been stored in the memory 2, the differential calculator 3 differentiates the fuel consuming characteristic models F.sub.1, F.sub.2 and F.sub.3 of the plants G.sub.1, G.sub.2 and G.sub.3 by the outputs P.sub.1, P.sub.2 and P.sub.3 of the plants G.sub.1, G.sub.2 and G.sub.3, respectively (see, FIGS. 20A-20C).
Each of the derivatives represents the increment of the fuel consumption against the increment of the output of each of the plants. EQU dF.sub.1 /dP.sub.1 =4P.sub.1 +3 (5) EQU dF.sub.2 /dP.sub.2 =2P.sub.2 +4 (6) EQU dF.sub.3 /dP.sub.3 =2P.sub.3 +1 (7)
When the differential calculator 3 has completed the differential calculation, the command value calculator 4 calculates the output command values P.sub.1 *, P.sub.2 * and P.sub.3 * of the plants G.sub.1, G.sub.2 and G.sub.3 on the basis of the derivatives fed from the differential calculator 3.
If estimated load amount L is eight, for example, the following equation holds because the sum total of the outputs P.sub.1, P.sub.2 and P.sub.3 of the plants G.sub.1, G.sub.2 and G.sub.3 must be eight. EQU L=P.sub.1 +P.sub.2 +P.sub.3 =8 (8)
On the other hand, the sum total of the fuel consumptions of the plants G.sub.m becomes minimum when the increment of the fuel consumption against the increment of the output P.sub.m of each plant G.sub.m coincides with that of all the other plants in the fixed-incremental fuel cost method. In other words, the following equations hold because the increment of the fuel consumption against the increment of the output P.sub.m of the plant G.sub.m coincide with that of the other plants if the derivatives output from the differential calculator 3 coincide with each other. EQU dF.sub.1 /dP.sub.1 =dF.sub.2 /dP.sub.2 =dF.sub.3 /dP.sub.3 EQU .thrfore. 4P.sub.1 +3=2P.sub.2 +4=2P.sub.3 +1 (9)
Thus, when the outputs P.sub.m of the plants G.sub.m satisfy both equations (8) and (9), the estimated load amount L can be achieved with a minimum fuel consumption. Accordingly, we calculate the outputs P.sub.m of the plants G.sub.m that satisfy equations (8) and (9).
In this case, the calculation results are P.sub.1 =1.5, P.sub.2 =2.5 and P.sub.3 =4 so that the output command values P.sub.1 *, P.sub.2 * and P.sub.3 * of the plants G.sub.1, G.sub.2 and G.sub.3 are decided as follows, and the minimum fuel consumption F.sub.min in this case takes the following value. EQU G.sub.1 .fwdarw.P.sub.1 *=1.5 F.sub.1 =10 EQU G.sub.2 .fwdarw.P.sub.2 *=2.5 F.sub.2 =18.25 EQU G.sub.3 .fwdarw.P.sub.3 *=4.0 F.sub.1 =26 EQU F.sub.min =F.sub.1 +F.sub.2 +F.sub.3 =54.25 (10)
Finally, the command value calculator 4 supplies the plants G.sub.1, G.sub.2 and G.sub.3 with the thus determined output command values P.sub.1 *, P.sub.2 * and P.sub.3 * of the plants G.sub.1, G.sub.2 and G.sub.3, and completes the processings.
In actual plants, however, there are some delays for the outputs of the plants to respond to the increments of the fuel supply for the plants. This often results in rather inaccurate output command values of the fuel consuming characteristic models employed in the conventional command value decision unit. In view of this, "On-line Economic Load Dispatch Based on Fuel Cost Dynamics", by M. Yoshikawa, N. Toshida, N. Nakajima, Y. Harada, M. Tsurugai, and Y. Nakata, IEEE Power Engineering Society, Winter Meeting, 96 WM 289-9 PWRS, applies, to generators as an example of plants, ARMA (AutoRegressive Moving Average)-model-supplemented quadratic model, a dynamic fuel consuming characteristic model capable of describing hysteresis characteristics of the revised ARMA model. It is expressed as EQU F.sub.m (t)=Q.sub.m (t)=aP.sub.m.sup.2 (t)+bP.sub.m (t)+c+eP.sub.m (t)+fP.sub.m (t-1)+gQ.sub.m (t-1)+h (11)
where P.sub.m (t) is the plant (generator) output at time t, P.sub.m (t-1) is the plant (generator) output at time t-1, and Q.sub.m (t-1) is the fuel consumption at the time t-1.
When employing equation (11) as the fuel consumption, the fuel consuming characteristic model cannot be decided at only a particular time point, and hence it becomes necessary to minimize the total fuel cost over a plurality of time points. In other words, the total fuel cost (objective function) to be minimized can be described by following equation (12). ##EQU1##
In equation (12), T is the number of the plurality of time points over which the total fuel cost should be minimized where the current time t=1, and M denotes the total number of the plants (generators).
Furthermore, when using equation (11), since the fixed-incremental fuel cost method cannot be applied without change, a method such as QP (Quadratic Programming) should be applied considering the constraints are linear. The constrains include supply and demand balance, upper and lower limits of the plant output, and constraint on the plant output rate, for example.
The conventional command value decision unit thus arranged has a problem in that the output command value P.sub.m * of each plant G.sub.m cannot be decided at high accuracy owing to deviations of the collected data or the response delay of the plants when using the static fuel consuming characteristic model F.sub.m obtained by the least squares method.
Moreover, when using the dynamic fuel consuming characteristic model which is a revised version of the ARMA model capable of describing the hysteresis characteristics as the fuel consuming characteristic model, it is necessary to apply the QP method or the like instead of the existing fixed-incremental fuel cost method. This, however, presents problems in that it takes a long time for calculation, and that the compatibility is lost with the conventional systems.